Dithering is a technique that can improve human perception of low-resolution data by reducing quantization artifacts. In this work we formalize and analytically justify two metrics for quantization artifact prominence, using them to design a novel dithering method for distortion-controlled data compression. We present theoretical entropy calculations for this dither and experimentally validate its performance on a low-rate image compression task. The result is a drastic improvement in the perceptual quality of quantized images with a lower recompression entropy than any state-of-the-art dither technique, achieving 45 points lower PIQUE at the same rate or 40% lower rate at the same PIQUE. The proposed dither is an adaptable tool applicable for use in any lossy compression system, permitting precise control of rate-distortion characteristics for both compression and recompression.